The short answer is yes, you can. Flat feet is no longer a disqualifying condition for military enlistment, provided that the enlistee does not show symptomatic flat feet. In short, this essentially means that if you are showing detrimental symptoms, you could be barred from enlisting in the military.

Can you not get drafted if you have flat feet?

You can't have flat feet

While someone who has flat feet can serve in the military, it depends on the severity. If someone has “symptomatic” flat feet, which indicates that the condition causes the person chronic physical pain, then he or she cannot serve.

Why couldn't you join the Army with flat feet?

Those with flat feet are not suited to marching - they can sustain spinal damage. The government may not care if one is killed, but cannot take the chance of anyone's seeking a disability pension.